Zel'dovich smearing approximation of the BAO feature for model-agnostic cosmological inference

TL;DR

This work develops a model-agnostic framework for inferring cosmology from the BAO feature in redshift space by combining a Zel'dovich smearing approximation with a scale-dependent bias plus mode coupling (sdbmc) model and a cosmology-independent BiSequential basis for the linear 2-point function. The approach employs a low-k observable set, including Σ^(ell)2, and modest weak ΛCDM priors to constrain parameters like the linear-point r_LP, the zero-crossing r_ZC, the smearing scale σ_v, and the growth-related quantity f, while accounting for degeneracies with the mode-coupling amplitude A_MC. In toy DESI LRG analyses, the framework yields unbiased parameter recovery with percent-level precision on r_LP (~0.8%) and r_ZC (~1.8%), and ~11% precision on σ_v and f, demonstrating that including sdbmc is essential to avoid biases that arise in no-sdbmc analyses. The methodology provides a data-ready pathway for model-agnostic BAO inference that can exploit full-shape information beyond traditional BAO summaries and is applicable to future datasets such as Ly-α, DESI, and 21 cm surveys, with extensions to account for fiducial-projection effects discussed for future work.

Abstract

A model-agnostic description of the baryon acoustic oscillation (BAO) feature in redshift space requires a number of ingredients. Physically, one must describe the impact of cosmological bulk flows which progressively and anisotropically smear out the feature over time. One must also model the effects of the scale dependence of tracer bias and the mode coupling between short and long scales. All of these can be incorporated using the Zel'dovich approximation alone, without reference to any particular cosmological model. On the technical front, one needs a robust, complete and cosmology-independent basis to describe the shape of the real space BAO feature in linear theory, which can then be propagated to the nonlinearly evolved, measured feature in redshift space. In this work, we describe how these ingredients -- which we have systematically constructed in recent work -- come together in an accurate framework capable of describing the BAO-scale pairwise measurements of state-of-the-art galaxy surveys. Using mock observations and $N$-body simulations, we show that our template-free framework can produce unbiased and precise cosmological constraints for samples with realistic levels of nonlinearity. This work represents one of the final steps in constructing a data-ready analysis framework for model-agnostic cosmological inference from the BAO feature.

Figures (8)

• Figure 1: Inference results for the toy DESI LRG sample.(Left panel): Constraints on cosmological parameters. Contours show the $68\%,95\%,99\%$ confidence regions. Dashed lines intersecting at white stars indicate the best fit parameter vector. Dotted lines intersecting at yellow stars indicate ground truth values. The diagonal panel titles give the median and $68\%$ confidence interval of the marginal constraints. We see unbiased recovery of all parameters at better than $95\%$ confidence. See Fig. \ref{['fig:contours']} for joint constraints on all varied parameters. (Right panel): Comparison of the data with the best fit model. Points with error bars show the mock data for $\Delta\hat{\xi}^{(\ell)}(s)$ (colour-coded for $\ell$ as indicated by the text labels) and $\hat{\Sigma}^{(\ell)2}$ (three blue points in the upper left, with $\ell=0,2,4$ from left to right). Colour-coded solid curves with error bands show the best fit and central $68\%$ confidence region from the parameter inference exercise for the 2pcf multipoles. The corresponding results for the power spectrum multipole integrals are shown by the cyan stars with asymmetric error bars. For clarity, we have given an additive offset of $+50 (h^{-1}{\rm Mpc})^2$ to each of the $\hat{\Sigma}^{(\ell)2}$ values and their corresponding best fit results. Colour-coded dotted curves show the effect of setting $A_{\rm MC}\to0$ in the solid curves while holding all other parameters at their best fit values; we see that this has a small effect on the location of the monopole peak and the shape of the quadrupole. The text label gives the value of $\chi^2$ for the best fit along with the number of degrees of freedom and corresponding $p$-value; the fit is of reasonable quality.
• Figure 2: Same as left panel of Fig. \ref{['fig:cosmofit']}, showing constraints on the sdbmc parameters (left panel) and a subset of cosmological and sdbmc parameters (right panel) to highlight some important degeneracies, notably $(A_{\rm MC},r_{\rm LP})$, $(B_{1\ast},r_{\rm LP})$, $(B_{v\ast},\sigma_{\rm v})$. We see unbiased recovery of all parameters at better than $95\%$ confidence. See text for a discussion and Fig. \ref{['fig:contours']} for joint constraints on all varied parameters.
• Figure 3: Reconstructed linear theory for the toy DESI LRG sample. Red solid curve shows the ground truth for $\xi_{\rm lin}(r)$. Dashed curves with error bands show the respective median and central $68\%$ confidence region from the inference exercise, while the correspondingly coloured solid curve shows the best fit. We see good agreement between the best fit, median and ground truth, with the ground truth remaining inside the inferred $68\%$ interval over the entire range of scales. See text for a discussion.
• Figure 4: Same as left panel of Fig. \ref{['fig:cosmofit']}, showing constraints on cosmological parameters using chains in which we fixed $A_{\rm MC}=0$(left panel) or set all sdbmc parameters to zero (right panel). We see a $\sim3\sigma$ bias in the recovery of the ground truth $r_{\rm LP}$ in the left panel, which increases dramatically in the right panel, now also affecting $\sigma_{\rm v}$. See text for a discussion.
• Figure 5: Multipoles of the non-linearly evolved redshift space dimensionless power spectrum (left panel) and 2pcf (right panel) for the HADES cosmology and sample described in the text. In each upper panel, solid curves show the exact sdbmc result, while dashed (dotted) curves show the polyLG (expLG) flavour of the Zel'dovich smearing approximation, all using the best fit values for the parameters $\{B_1,B_v,A_{\rm MC}\}$ from Table 1 of ps25b. The text label in the left upper panel gives the value of $\sigma$ (equation \ref{['eq:sigma-def']}). The lower panels show the corresponding residuals (i.e., approximate/exact - 1), while the horizontal dotted lines indicate $\pm5\%$ deviations. The curves in the left panel used the various exact and approximate Fourier space results discussed in the text, while those in the right panel were computed as the Hankel transforms $\xi^{(\ell)}(s)=i^\ell\int{\rm d}\ln k\,\Delta^{(\ell)2}(k)j_\ell(ks)$ of the corresponding curves from the left panel. The polyLG flavour clearly outperforms the expLG flavour in describing the sdbmc result, especially for $\ell=2,4$.